(3y-12)(y-5)=0

Solution for (3y-12)(y-5)=0 equation:

Simplifying
(3y + -12)(y + -5) = 0

Reorder the terms:
(-12 + 3y)(y + -5) = 0

Reorder the terms:
(-12 + 3y)(-5 + y) = 0

Multiply (-12 + 3y) * (-5 + y)
(-12(-5 + y) + 3y * (-5 + y)) = 0
((-5 * -12 + y * -12) + 3y * (-5 + y)) = 0
((60 + -12y) + 3y * (-5 + y)) = 0
(60 + -12y + (-5 * 3y + y * 3y)) = 0
(60 + -12y + (-15y + 3y2)) = 0

Combine like terms: -12y + -15y = -27y
(60 + -27y + 3y2) = 0

Solving
60 + -27y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -9y + y2) = 0

Factor a trinomial.
3((4 + -1y)(5 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {4, 5}